# Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes

## TL;DR

This paper introduces a new method for constructing optimal sliced Latin hypercube designs with arbitrary run sizes, improving space-filling properties and flexibility in experimental design.

## Contribution

It proposes a novel construction method and a combined space-filling measurement for SLHDs with arbitrary run sizes, along with algorithms to find optimal designs.

## Key findings

- Effective construction of SLHDs with arbitrary run sizes demonstrated
- New space-filling measurement improves design quality
- Algorithms successfully identify optimal designs in examples

## Abstract

Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However, most existing methods for constructing optimal SLHDs have restriction on the run sizes. In this paper, we propose a new method for constructing SLHDs with arbitrary run sizes, and a new combined space-filling measurement describing the space-filling property for both the whole design and its slices. Furthermore, we develop general algorithms to search the optimal SLHD with arbitrary run sizes under the proposed measurement. Examples are presented to illustrate that effectiveness of the proposed methods.